Optimization in Machine Learning:a Distribution-Space Approach

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space,but with a non-convex constraint set introduced by model parameterization.This observation allows us to repose such problems via a suitable relaxation as convex optimization problems in the space of distributions over the training parameters.We derive some simple relationships between the distribution-space problem and the original problem,e.g.,a distribution-space solution is at least as good as a solution in the original space.Moreover,we develop a numerical algorithm based on mixture distributions to perform approximate optimization directly in the distribution space.Consistency of this approximation is established and the numerical efficacy of the proposed algorithm is illustrated in simple examples.In both theory and practice,this formulation provides an alternative approach to large-scale optimization in machine learning.

Characteristics and influencing mechanisms of production-living-ecological space dynamics in the Three Gorges Reservoir Area(TGRA),Chongqing,China

The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of production-living-ecological spaces for sustainable and high-quality development in the TGRA.This study investigated the dynamic variation of production-living-ecological spaces in the TGRA by employing land use data in 2000,2005,2010,2015,and 2018,and detected the influencing factors by using the Geographic detector(GeoDetector).Results implied that the structure and dynamic trajectories of production-living-ecological spaces in the TGRA varied in both horizontal and vertical directions,and the study area was dominated by ecological space.A spatial orientation towards the northeast was detected in the evolution of production-living-ecological spaces during 2000-2018.In terms of quantity,the transition from ecological space(grassland and woodland)to agriculture land accounted for the largest proportion from 2000 to 2018.However,the reverse transition from agriculture land to ecological space has increased since 2000 with the efforts of“Grain for Green”.In terms of temporal scale,there was a fluctuating trend in production space with the continuous expansion of living space,while ecological space showed an inverted U-shaped trend during 2000-2018.The dynamic pattern of production-living-ecological spaces in the TGRA was influenced by both physical and socio-economic variables as basic determinants and dominant driving factors,respectively.Finally,the harmonization and protection of production-living-ecological spaces still require policy-makers’efforts.This work may have potential in advancing our understanding about land use conflicts,and provide a reference for rational layout of spatial functions and the realization of sustainable development in the TGRA.

Research on Adaptability Analysis of Environmental Space Demand and Design Optimization of Daycare Centers: Taking Chongqing’s Community F as an Example

Currently,there is a lack of research on the detailed environmental spatial design of community daycare centers at the micro level.This study focuses on Community F in Chongqing,using the elderly’s“willingness to demand”as a central aspect.It examines indoor and outdoor environmental space needs at a micro level,considering both functional requirements and spiritual needs based on existing research.The analysis incorporates three adaptive elements:current construction,surrounding environment,and operational management.It explores the feasibility of restructuring spatial layouts,utilizing local resources,and integrating Bayu cultural characteristics.Finally,through design optimization practices,the study proposes three strategies for aging optimization:functional integration and interaction,user-friendly facilities,and emotional connections to place.

Horizontal well spacing optimization and gas injection simulation for the ultra-low-permeability Yongjin reservoir

Optimal spacing for vertical wells can be effectively predicted with several published methods,but methods suitable for assessing the proper horizontal well spacing are rare.This work proposes a method for calculating the optimal horizontal well spacing for an ultra-low permeability reservoir e the Yongjin reservoir in the Juggar Basin,northwestern China.The result shows that a spacing of 640m is the most economical for the development of the reservoir.To better develop the reservoir,simulation approaches are used and a new model is built based on the calculated well spacing.Since the reservoir has an ultralow permeability,gas injection is regarded as the preferred enhanced oil recovery(EOR)method.Injection of different gases including carbon dioxide,methane,nitrogen and mixed gas are modelled.The results show that carbon dioxide injection is the most efficient and economical for the development of the reservoir.However,if the reservoir produces enough methane,reinjecting methane is even better than injecting carbon dioxide.

Research on Optimal Design of Campus Space Based on POE Concept: A Case Study of Anhui Xinhua College

Through the analysis of the overall landscape,revetments and roads and plant landscape,10 evaluation factors were determined.The comprehensive evaluation model for the campus space of Anhui Xinhua University was constructed by analytic hierarchy process(AHP).The results showed that revetment safety,road convenience,plant disease resistance and campus activity space were important factors affecting the spatial form planning of campus.Through the comparative analysis of the collected data,optimization suggestions were put forward to provide a basis for the establishment of“people-oriented”campus open space system.

OPTIMAL BIRKHOFF INTERPOLATION AND BIRKHOFF NUMBERS IN SOME FUNCTION SPACES

This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.

Optimization Strategies of Beijing Elderly Care Service Stations Based on Questionnaire Survey Method: A Case Study of Zhanlan Road Street of Xicheng District

4 elderly care service stations in Zhanlan Road Street,Xicheng District,Beijing are selected,and questionnaires are designed and distributed to the surrounding elderly population to understand their needs and satisfaction with the station environment.By observing elderly care service stations on site,the characteristics,obstacles,and shortcomings of the environment are recorded,and relevant data are collected and analyzed,such as the characteristics of the elderly population being interviewed,the planning and design data of the station environment,and the distribution of service facilities.The overall characteristics of the spatial environment of elderly care stations are summarized,and renovation measures and optimization suggestions are provided for the current shortcomings,thereby providing some basis for the spatial design of community elderly care service stations in the future.

Optimization Strategy for Passive Form Design of Architectural Grey Space under the Background of Climate Adaptability

Taking the bottom grey space with great influence on outdoor thermal comfort as the research object,this paper summarizes the morphological characteristics and climate response methods of two types of bottom grey space:overhead grey space and canopy grey space.The spatial form indexes that greatly affect the ecological performance of architectural grey space such as ventilation,shading,etc.are discussed,and two passive spatial form indexes of spatial scale and location orientation are studied.According to the research of related scholars and literature summary,the optimization strategies for passive form design of architectural grey space based on climate adaptability are put forward,which will provide a reference for the climate adaptive design of architectural grey space,and helps to improve the outdoor thermal environment from the micro scale and create a better living environment.

Optimization Transmission Theory and Technical Pathways that Describe Multiscale Urban Agglomeration Spaces

Urban agglomerations are spatial entities that promote the development of ‘new urbanization' processes within China. In this context, the concept of ‘multiscale urban agglomeration spaces' encompasses three linked levels: macroscale urban agglomerations, mesoscale cities, and microscale urban centers. Applying a series of multidisciplinary integrated research methods drawn from geography, urban planning, and architecture, this paper reveals two intensive utilization laws that can be generalized to apply to multiscale urban agglomeration spaces, top-to-bottom ‘positive transmission' linkage and inside-to-outside ‘negative transmission' movement. This paper also proposes optimization transmission theory and policy decision technical pathways that can be applied to these three urban agglomeration spatial scales. Specific technical pathways of transmission include intensive expansion and simulated decision-making in macroscale urban agglomerations, ecology, production, and living space intensive layout and dynamic decision-making in mesoscale cities, and four cores(i.e., ‘single, ring, axis, and pole core') progressive linkage and intensive optimization decision-making in microscale urban centers. The theory and technical pathways proposed in this paper solve the technical problem of optimization and provide intensive methods that can be applied not only at the individual level but also at multiple scales in urban agglomeration spaces. This study also advances a series of comprehensive technical solutions that can be applied to both compact and smart growth cities as well as to urban agglomerations. Solid theoretical support is provided for the optimization of Chinese land development, urbanization, agricultural development, and ecological security.

NONCOMPACT INFINITE OPTIMIZATION AND EQUILIBRIA OF CONSTRAINED GAMES IN GENERALIZED CONVEX SPACES

By applying a new existence theorem of quasi-equilibrium problems due to the author, some existence theorems of solutions for noncompact infinite optimization problems and noncompact constrained game problems are proved in generalized convex spaces without linear structure. These theorems improve and generalize a number of important results in recent literature.

Research on the Optimization of Public Spaces in Urban Villages Based on Space Syntax:A Case Study of Luochengtou Village in Handan City

This paper based on the theory of space syntax took Luochengtou Village in Handan City,Hebei Province for example,tried to figure out a proper way for the renewal of urban villages,and change the current dilemma of"one-size-fits-all"and"removing all"in most cases,and put forward that local conditions and regional characteristics must be considered to propose the renewal strategies more suitable for the targeted objects.Based on the space syntax Depthmap software and field investigation,the paper analyzed the accessibility,intelligibility and throughput of public spaces in Luochengtou Village,and put forward 3 optimization strategies in view of the problems such as insufficient public spaces,poor accessibility and intelligibility of roads,and poor activity of spaces,specifically,increasing public activity spaces,sorting out public space network,and creating active space nodes,so as to optimize public environment of the village,enhance villagers’sense of belonging,sense of safety and sense of identity.

Study on the Integration and Optimization of Campus Spaces: A Case Study of Yaohu Campus of Jiangxi Normal University

In view of the problems brought by blind expansion of campus, such as lack of public spaces, oversized spaces, and improper traffic designs, this paper took Yaohu Campus of Jiangxi Normal University for example, proposed the methods for integrating and optimizing campus spaces, such as establishing artistic conception of campus space, improving campus traffic organization, creating and improving the external communication spaces, on the basis of analyzing evolution history of campus spaces.

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

Optimization Design of Open Spaces Based on Wind Tunnel and CFD Simulation： Case Study of a Street Canyon in Northern China

Airflow in open spaces can significantly affect spatial quality. Therefore, according to the type of building structures, the airflow also has different forms. Studies have been conducted on the relation between airflow and pedestrian comfort; however, only few of them have focused on comprehensive urban planning that considers different weather conditions and people＇s ability to adapt. This research focuses on the differences in wind conditions caused by different spatial forms in different seasons. On the basis of a field survey in both summer and winter in a public open space, evaluation standards developed from environmental meteorological data and public feedback were used to evaluate simulation results. Next, several assumptions about canyon orientation and building types were proposed. Wind tunnel and CFD （computational fluid dynamics） simulations were conducted to evaluate the assumptions. The results showed that the canyon orientation significantly affected overall wind conditions and different building structures affected airflow. This research also provides a method to evaluate urban areas that have complicated wind environments.

Optimization Analysis of Campus Topic Space in Colleges and Universities——A Case Study of the Colleges and Universities in Lishui, Zhejiang Province

University campus is the most important place for life, study, activity and experience of contemporary college students. It is helpful for students to survive and develop to create the topic space of campus. Taking the topic space of college campuses in Lishui City of Zhejiang Province as an example, the current situations are analyzed through questionnaire survey and field visit. The results show that uni- versity campus space needs a clear topic; the demands are generally large for the topics of exchange and communication, learning and thinking, sports and leisure in all kinds of space; the creation of these types of topic spaces should focus on the peaceful environment, beautiful scenery, privacy of the space and WlFI coverage.

Metamodel-based Global Optimization Using Fuzzy Clustering for Design Space Reduction

High fidelity analysis are utilized in modern engineering design optimization problems which involve expensive black-box models.For computation-intensive engineering design problems,efficient global optimization methods must be developed to relieve the computational burden.A new metamodel-based global optimization method using fuzzy clustering for design space reduction(MGO-FCR) is presented.The uniformly distributed initial sample points are generated by Latin hypercube design to construct the radial basis function metamodel,whose accuracy is improved with increasing number of sample points gradually.Fuzzy c-mean method and Gath-Geva clustering method are applied to divide the design space into several small interesting cluster spaces for low and high dimensional problems respectively.Modeling efficiency and accuracy are directly related to the design space,so unconcerned spaces are eliminated by the proposed reduction principle and two pseudo reduction algorithms.The reduction principle is developed to determine whether the current design space should be reduced and which space is eliminated.The first pseudo reduction algorithm improves the speed of clustering,while the second pseudo reduction algorithm ensures the design space to be reduced.Through several numerical benchmark functions,comparative studies with adaptive response surface method,approximated unimodal region elimination method and mode-pursuing sampling are carried out.The optimization results reveal that this method captures the real global optimum for all the numerical benchmark functions.And the number of function evaluations show that the efficiency of this method is favorable especially for high dimensional problems.Based on this global design optimization method,a design optimization of a lifting surface in high speed flow is carried out and this method saves about 10 h compared with genetic algorithms.This method possesses favorable performance on efficiency,robustness and capability of global convergence and gives a new optimization strategy for engineering design optimization problems involving expensive black box models.

An adaptive ant colony system algorithm for continuous-space optimization problems

Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates.Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.

Reliable Space Pursuing for Reliability-based Design Optimization with Black-box Performance Functions

Reliability-based design optimization （RBDO） is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a ＂black-box＂ and their gradients are not available or not reliable. On the basis of the reliable design space （RDS） concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing （RSP） approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.

Optimization Design and Comprehensive Evaluation of Screw Contact of Space Battery Based on ANSYS

In order to improve the safety of the battery of satellite side mounting,and prevent the screw from producing excess due to frequent assembly and disassembly,the YS-20 material replacement and structure optimization design of the screw body are carried out under the premise of not changing the original tooling.The double⁃shear test of YS-20 bar is carried out,and the ANSYS optimization design module is used to design 7×7×6,a total of 294,calculation cases of D1,D2,T,the three important dimension parameters of screw structure.The actual bearing state of screw composite structure is accurately simulated by using asymmetric contact model.Three comprehensive evaluations are established,and the calculation examples satisfying the conditions are evaluated comprehensively.The final results are T=12.2 mm,D1=16 mm,D2=2 mm.The stress verification and contact analysis are carried out for the final scheme and the bearing state and contact state optimized screw structure are obtained.

Optimal Design of Street-side Green Spaces: A Case Study of Tiaoshan Cultural Park in Yuncheng City, Shanxi Province

Street-side green spaces are located by urban roads, serving neighboring residents and business population, they are public spaces for citizens working, relaxing and communicating with each other. Landscape design of street-side green spaces is the manifestation of city culture, history and development. Through investigating actual conditions, cultural and historical context, and neighboring traffic of Tiaoshan Cultural Park, this study summarizes deficiencies of the original plant and landscape setting designs, and proposes optimal designs of the park according to the design principles of street-side green spaces.